Palo 面试真题解析：Course Schedule II 拓扑排序

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

For example, the pair [0, 1] indicates that to take course 0 you have to first take course 1.

Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them.

If it is impossible to finish all courses, return an empty array.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]
Output: [0,1]
Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].

Example 2:

Input: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
Output: [0,2,1,3]
Explanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].

Example 3:

Input: numCourses = 1, prerequisites = []
Output: [0]

这道题要求根据先修关系输出一组可行的修课顺序，本质上是经典的拓扑排序问题。我们可以把每门课看成图中的节点，把“先修课 → 目标课”看成有向边，再用 Kahn 算法（BFS + 入度数组）或 DFS 三色标记来判断是否存在环；如果图中有环，就说明无法完成所有课程，直接返回空数组。题目还允许返回任意一种合法顺序，因此只要保证每门课都在它的所有先修课之后出现即可。